3D physics-based numerical scenarios for earthquake strong ground motion prediction : the case of the San Ramon fault in Santiago de Chile basin

(1)

(2)

(3)

iii

To my mother, Fabiola. For her inexhaustible love and support. A mi madre, Fabiola. Por su inagotable amor y apoyo.

(4)

(5)

v

Acknowledgement

In first place, I want to render thanks to my supervisor, professoressa Chiara Smerzini, for the incredible opportunity she gave to me to study (almost from scratch) such an interesting subject as it is engineering seismology, with access to such advanced tools and approach at the frontier of this knowledge, and if it was not enough, to apply this knowledge to a case study of my hometown, Santiago de Chile. Her mentoring, advice, support and comprehension given to me during all this process is invaluable, and I will always be grateful with her for all the energy she spent for me to improve and learn all the possible in this rather few months available. Thank you very much, professor, for this vote of confidence on me.

I want to thank also to my co-supervisor Maria Infantino for all the time and dedication spent to me, for the technical support and advice during this steep learning curve process I have been passed through these months.

I feel deeply proud for the opportunity to work and learn from such skilled and clever women. Thank you to professor Roberto Paolucci for directing me to my supervisor and this subject when I firstly asked him for thesis proposal, and also for the crucial advices given to me during my result analysis process.

Thanks to all friends and relatives that have put their “grain of sand”, giving me support, advices and have helped me in one way or another during this enriching process of living and studying abroad.

Deep thanks to my special woman, the one that took my hearth and change my life in the middle of this process, turning this experience into something amazing, into a dream we can share together. Thank you to my future wife Daniela, for all the support and energy you have put on me.

Thanks to my father, Esteban, for all the support and positiveness he has given me during this stage, as has also been all my life.

(6)

vi

Last but not least, to the woman who has devoted all her life to me, and to which I owe everything. Definitely, the most remarkable lesson I have learned during all this experience is the infinite love that a mother feels for their sons. It is so huge, that when the closer I have felt her is when the farther I have been from her, and when the more I have missed someone, is when the most present she has been to me. Eternal acknowledgements to my mother, Fabiola, without her, anything of this would have been possible. I love you.

(7)

vii

Abstract

The main aim of this study is to produce deterministic seismic scenarios using an advanced approach based on three-dimensional physics-based numerical simulations (3DPBNS) to characterize strong ground motion from source-to-site in the large urban area of Santiago de Chile due to the seismic hazard of the San Ramón Fault. The 3DPBNS were performed using the open-source software SPEED based on the Discontinuous Garlekin Spectral Element method (Mazzieri, et al., 2013)

Because of the limited frequency range of this approach, numerical simulations have to be post-processed with a novel approach based on artificial neural networks (ANN2BB, after Paolucci et al (2018)) to enrich the response in a frequency range for engineering purposes (0 to 25Hz). Numerical scenarios are presented for different magnitudes (from Mw6.0 to Mw7.0) and cyclic soil response (linear visco-elastic and non-linear visco-elastic behavior of shear modulus and damping ratio), in form of peak ground velocity maps (PGV), peak ground acceleration maps (PGA) and pseudo-acceleration maps for several response periods. This results are compared with classical GMPE method to highlight its main features, such as better near-source response characterization, full spatial correlation and physical seismic source features as directivity and radiation patterns.

Main results demonstrate the strong ability of 3DPBNS+ANN2BB to describe spatial variability of earthquake ground motion due to topographical, site and seismic source effects for different magnitudes and a wide range of frequencies, as reasonable peak-distance attenuation agreements between this method and GMPE, noticing in peak maps a much better description capacity of near-source effects for 3DPBNS and spatial correlation. For non-linear visco-elastic soil behavior, very limited differences with respect to the linear-elastic case are observed, due to the stiff coarse gravel predominant in the Santiago basin.

A discussion of the current Chilean regulation for structural seismic design is proposed, making a simple comparison between scenario-based response spectrum and design spectrum from the

(8)

viii

regulations on selected sites, showing that a single scenario can significantly surpass the elastic design spectrum of the regulation for all range of periods in some cases.

Keywords: earthquakes, strong ground motion, 3D physics-based numerical simulations, Santiago de Chile.

(9)

ix

List of Figures

Figure 1: overall economic losses (green) and insured economic loss (blue) for

earthquake/tsunami events worldwide 2008-2018 (Munich Re, 2019). ... 2

Figure 2: number of relevant earthquakes/tsunamis (up) and catastrophic earthquakes/tsunamis (down) per year in period 2008-2018 (Munich Re, 2019). ... 3

Figure 3: convolution of hazard, vulnerability and exposure. Seismic risk. (Lai, et al., 2009)... 9

Figure 4: four-step process for DSHA (Kramer, 2014). ... 11

Figure 5: four-step process for PSHA (Kramer, 2014) ... 11

Figure 6: GMP models timeline, level of detail and relationship (Douglas, et al., 2008). ... 14

Figure 7: simulation scheme of SPEED (Paolucci, et al., 2018). ... 18

Figure 8: kinematic modelling of seismic source (Paolucci, et al., 2018). ... 19

Figure 9: scheme of construction of broadband response using ANN (Paolucci, et al., 2018). ... 21

Figure 10: workflow of ground shaking maps production using SPEED (Paolucci, et al., 2018). . 21

Figure 11: tectonic plates in Chile. The not-labeled blue plate on bottom correspond to the Antarctic plate, which defines the seismic hazard in the southern zone of Chile. ... 22

Figure 12: typical continental subduction zone section. ... 23

Figure 13: types of earthquakes in central zone of Chile. National Seismologic Center http://www.csn.uchile.cl . ... 23

Figure 14: 3D view of Santiago de Chile Basin and the WAT (Armijo, et al., 2010). ... 25

Figure 15: top view and sections of the SRF (Armijo, et al., 2010). ... 26

Figure 16: geological elevation of the WAT and SRF (Armijo, et al., 2010). ... 27

Figure 17: Santiago model with size, wave velocities, density and quality factors specifications (POLIMI-Munich Re Contract, 2014). ... 28

Figure 18: on top, basin of Santiago de Chile, in the back rectangle the study area of Pilz et al (2010) and the the black lines are section of the 3D shear wave model with bedrock level in grey and Vs values in colors shown below. ... 29

Figure 19: Thickness of sedimentary cove of the basin of Santiago de Chile shown in color bar, determined by interpolation of gravimetric data (PIlz, et al., 2011). ... 30

Figure 20: model elevation view with mesh relative sizes (left). Model plant view with monitors distributions (right). ... 31

Figure 21: 3D view of SRF in Santiago model. ... 32

Figure 22: linear equivalent model for shear modulus reduction (Kramer, 2014). ... 32

Figure 23: surface geology of Santiago basin (Leyton, et al., 2010). ... 33

Figure 24: shear modulus reduction and damping ratio increase for granular soils (Rodriguez, et al., 1995). Red lines indicates non-linear visco-elastic behavior adopted for this study. ... 34

Figure 25: active fault of scenario E15 showing the slip distribution and hypocenter with red star (left). Relative position of the active fault respect to the maximum credible area of rupture (right). Length represent horizontal distance, while width is vertical distance. ... 39 Figure 26: Peak maps of geometric mean of components (gmh) scenario E15 from top to

(12)

xii

while the blue rectangle is the top view projection of the fault. The black star represents the projection of the hypocenter. ... 40 Figure 27: vertical component of PGV for scenario E15. ... 41 Figure 28: scenario E15 velocity time histories for selected site (in cyan circles) superimposed on PGV map for EW component. ... 41 Figure 29: scenario E15 velocity time histories for selected site (in cyan circles) superimposed on PGV map for NS component. ... 42 Figure 30: scenario E15 velocity time histories for selected site (in cyan circles) superimposed on PGV map for UD component. ... 42 Figure 31: on the left side, three components of velocity time-histories for scenario E15. On the right side, Fourier amplitude spectra of the same components for each selected site. ... 43 Figure 32: active fault of scenario E16 showing the slip distribution and hypocenter with red star (left). Relative position of the active fault respect to the maximum credible area of rupture (right). Length represent horizontal distance, while width is vertical distance. ... 44 Figure 33: Peak maps of geometric mean of components (gmh) scenario E16 from top to

bottom and left to right: PGV, PGA, PSA at 0.3s, 0.5s, 1s, 2s. The light black line is the basin, while the blue rectangle is the top view projection of the fault. The black star represents the projection of the hypocenter. ... 45 Figure 34: vertical component of PGV for scenario E16. ... 46 Figure 35: scenario E16 velocity time histories for selected site (in cyan circles) superimposed on PGV map for EW component. ... 46 Figure 36: scenario E16 velocity time histories for selected site (in cyan circles) superimposed on PGV map for NS component. ... 47 Figure 37: scenario E16 velocity time histories for selected site (in cyan circles) superimposed on PGV map for UD component. ... 47 Figure 38: on the left side, three components of velocity time-histories for scenario E16. On the right side, Fourier amplitude spectra of the same components for each selected site. ... 48 Figure 39: active fault of scenario E13 showing the slip distribution and hypocenter with red star (left). Relative position of the active fault respect to the maximum credible area of rupture (right). Length represent horizontal distance, while width is vertical distance. ... 49 Figure 40: Peak maps of geometric mean of components (gmh) scenario E13 from top to

bottom and left to right: PGV, PGA, PSA at 0.3s, 0.5s, 1s, 2s. The light black line is the basin, while the blue rectangle is the top view projection of the fault. The black star represents the projection of the hypocenter ... 50 Figure 41: vertical component of PGV for scenario E13. ... 51 Figure 42: scenario E13 velocity time histories for selected site (in cyan circles) superimposed on PGV map for EW component. ... 51 Figure 43: scenario E13 velocity time histories for selected site (in cyan circles) superimposed on PGV map for NS component. ... 52 Figure 44: scenario E13 velocity time histories for selected site (in cyan circles) superimposed on PGV map for UD component. ... 52

(13)

xiii

Figure 45: on the left side, three components of velocity time-histories for scenario E13. On the right side, Fourier amplitude spectra of the same components for each selected site. ... 53 Figure 46: active fault of scenario E14 showing the slip distribution and hypocenter with red star (left). Relative position of the active fault respect to the maximum credible area of rupture (right). Length represent horizontal distance, while width is vertical distance. ... 54 Figure 47: Peak maps of geometric mean of components (gmh) scenario E14 from top to

bottom and left to right: PGV, PGA, PSA at 0.3s, 0.5s, 1s, 2s. The light black line is the basin, while the blue rectangle is the top view projection of the fault. The black star represents the projection of the hypocenter. ... 55 Figure 48: vertical component of PGV for scenario E14. ... 56 Figure 49: : scenario E14 velocity time histories for selected site (in cyan circles) superimposed on PGV map for EW component. ... 56 Figure 50: : scenario E14 velocity time histories for selected site (in cyan circles) superimposed on PGV map for NS component. ... 57 Figure 51: scenario E14 velocity time histories for selected site (in cyan circles) superimposed on PGV map for UD component. ... 57 Figure 52: on the left side, three components of velocity time-histories for scenario E14. On the right side, Fourier amplitude spectra of the same components for each selected site. ... 58 Figure 53: PGV vs distance charts for scenario E15 (first row), E16 (second row) and E13 (third row). Left column are peak-distance plot for monitors within the basin area, while right column are charts of monitors outside the basin. Black dots are individual simulations per monitor, Red line is the mean trend of the dispersion, while blue line is the GMPE CAEA15 trend. ... 61 Figure 54: PGV maps (of gmh) on top from left to right: scenarios E15 (Mw6.0), E16 (Mw6.5) and E13 (Mw7.0). Below each scenario, the GMPE maps associated. ... 62 Figure 55: PGA vs distance charts for scenario E15 (first row), E16 (second row) and E13 (third row). Left column are peak-distance plot for monitors within the basin area, while right column are charts of monitors outside the basin. Black dots are individual simulations per monitor, Red line is the mean trend of the dispersion, while blue line is the GMPE CAEA15 trend. ... 64 Figure 56: PGA maps (of gmh) on top from left to right: scenarios E15 (Mw6.0), E16 (Mw6.5) and E13 (Mw7.0). Below each scenario, the GMPE maps associated. ... 65 Figure 57: on the left, Manquehue site velocity time histories of E13 LE (black line) and E14 NLE (red line). On the right, Fourier amplitude spectra for E13 LE (black line) and E14 NLE (red line). ... 68 Figure 58: on the left, Bajos de Mena site velocity time histories of E13 LE (black line) and E14 NLE (red line). On the right, Fourier amplitude spectra for E13 LE (black line) and E14 NLE (red line). ... 69 Figure 59: on top from left to right: PGV maps (of gmh) for E13 (LE), E14 (NLE) and GMPE for Mw 7.0. Below from left to right: PGA maps for E13 (LE), E14 (NLE) and GMPE for Mw7.0. ... 70 Figure 60: on top from left to right: PSA maps (of gmh) at T=0.3s for E13 (LE), E14 (NLE) and GMPE for Mw 7.0. Below from left to right: PSA maps at T=0.5s for E13 (LE), E14 (NLE) and GMPE for Mw7.0. ... 71

(14)

xiv

Figure 61: on top from left to right: PSA maps (of gmh) at T=0.75s for E13 (LE), E14 (NLE) and GMPE for Mw 7.0. Below from left to right: PSA maps at T=1.0s for E13 (LE), E14 (NLE) and GMPE for Mw7.0 ... 72 Figure 62: active fault of scenario E11 showing the slip distribution and hypocenter with red star (left). Relative position of the active fault respect to the maximum credible area of rupture (right). Length represent horizontal distance, while width is vertical distance. ... 73 Figure 63: modes of rupture for shear fault (left) rupture velocity domain and boundaries to describe directivity effect of sub-shear and super-shear rupture velocity. Adapted from

Madariaga (2007) and Durham (2007). ... 76 Figure 64: PGV maps (of gmh) scenarios E13 (left) and E11 (right) with same intermediate class break classification for comparison purposes. Below, the correspondent slip distributions of the fault in [m/s]. the red star denotes the hypocenter location. ... 77 Figure 65: PGV map (of gmh) for E11 scenario (left) In the near source range. On the right, three component of time history for velocity of the monitor with highest peak values (1st_{column) and}

displacement (2nd_{column)... 78}

Figure 66: rupture velocity distribution in the active fault in [m/s]. the red star denotes the hypocenter location. ... 78 Figure 67: seismic zones maps of Chile, from left to right: north, center and south (NCh433 and NCh2369). ... 84 Figure 68: comparative charts of scenario based pseudo-acceleration response spectra

(3DPBNS+ANN2BB in red and GMPE CAEA15 in black) and design spectra (NCh433 in blue and NCh2369 in green) for 3 sites within Santiago basin (Manquehue, Bajos de Mena and La Moneda) and 2 sites out of the basin (Cerro San Cristobal and Lo Prado Tunnel) Minimum distances site-rupture are presented below the each legend. ... 85

(15)

xv

List of Tables

Table 1: losses and fatalities of five costliest earthquakes in period 2008-2018 (Munich Re,

2019) ... 2

Table 2: seismic scenarios description. HER refers to Herrero and Bernard (1994) rupture generator. ... 35

Table 3: Scenarios features. ... 36

Table 4: main information of selected sites. ... 38

Table 5: main features scenario E11. ... 73

(16)

1

1 Introduction

1.1 Motivation

Seismic risk is, in a wide sense, the earthquake-induced social and/or economic expected losses at a site or within an area, during a specific time. It is usually computed as the combination of three factors: seismic hazard (the quantitative evaluation of the expected ground motion in a site), vulnerability (the expected amount of damage to a structure or system in a site) and exposure (the expected economic or social impact induced by the seismic event to the system). Seismic risk has been a matter of increasing attention in the last century, transcending the awareness of such events from local to national or multinational interest, due to thousands of lives that are lost each year, including the loss of properties, negative economic consequences and social impact this event can cause. In increasingly larger and more complex cities, often associated with an uncontrolled increase in urban population, urban centers in seismic areas have become more vulnerable and exposed, so that the risk associated with such events is growing.

Just in the period 2008-2018, 444 relevant earthquakes-tsunamis events worldwide occurred, 36 of which have been catastrophic (Munich Re, 2019), giving an average of more than three catastrophic seismic events per year Figure 2. Table 1 shows the overall tangible loss due to seismic events during this period is around US$ 477 Billion, from where only US$ 83.7 Billion (17.5%) corresponded to ensured losses (Figure 1), but this does not consider the intangible economic loss, such as lack of production and good exchanges due to infrastructure damage, social disruption and additional recovery costs to society. To illustrate the extent damage that a single event can produce,

Table 1 shows the five costliest earthquakes/tsunamis in the last 10 years, among which is the Mw 9.1 Tohoku earthquake in Japan (the costliest), Mw 7.9 Sichuan earthquake in China (the deadliest) and Mw 8.8 Maule earthquake in Chile, among others.

(17)

2

Table 1: losses and fatalities of five costliest earthquakes in period 2008-2018 (Munich Re, 2019)

five Costliest earthquake/tsunami events worldwide 2008-2018 ordered by inflation adjusted overall losses

date Country event Overall

losses [US$m] Insured losses [US$m] Fatalities

11-Mar-11 Japan Earthquake, tsunami

157,000 29,800 15,880

12-May-08 China Earthquake 107,000 380 87,149

16-Apr-16 Japan Earthquake 31,400 6,400 205

27-Feb-10 Chile Earthquake, tsunami

30,100 8,000 520

22-Feb-11 New Zealand Earthquake 22,700 15,600 185

Figure 1: overall economic losses (green) and insured economic loss (blue) for earthquake/tsunami events worldwide 2008-2018 (Munich Re, 2019).

(18)

3

Figure 2: number of relevant earthquakes/tsunamis (up) and catastrophic earthquakes/tsunamis (down) per year in period 2008-2018 (Munich Re, 2019).

Due to the high loss due to earthquakes, seismic risk management have become a social and economic priority to enhance sustainable economic development over time, preparing all the sectors of society with all the resources needed to face with disaster, aftershock and recovery stages better. A key component for an effective disaster risk management is represented by an accurate assessment of seismic risk. Seismic risk assessment aims at predicting the social and economic expected losses within a given area, during a specific time frame, due to earthquakes.

(19)

4

The assessment of potential impacts is not a trivial task, as it requires important agreements and efforts from all the stakeholders and the society, not transferable entirely from one country to another, or even from one city to another in the same country, because of the different geographical allocation, economic activities, infrastructure development, vulnerabilities, level of exposure, and the hazard source.

From the engineering point of view (i.e. structural design, geotechnics, engineering seismology, civil engineering disciplines), seismic hazard is the key aspect to identify and assess prior to planning, projection and construction building and infrastructure. Basically, seismic hazard assessment identifies the likelihood of a given level of ground shaking across a region, within a specific time frame. This is a fundamental component in hazard mapping for design codes and seismic risk assessment (Poljanksek, 2017). Tools for Earthquake Ground Motion Prediction (EGMP) is a key component in seismic hazard assessment studies, both within probabilistic and deterministic frameworks, and have the goal of providing estimates of the expected level of ground motion intensity measures (e.g. Peak Ground Acceleration), as a function of explanatory variables, such as magnitude, distance and site conditions.

Nowadays, a variety of tools for EGMP exists, with different levels of complexity, data/input parameters needed, output parameters and outcomes for either academic and engineering purposes. Douglas & Aochi (2008) present a comprehensive survey with techniques for EGMP, showing the advantages and limitations comparatively for engineering purposes. Among them, the most used for engineering design and seismic risk assessment are the ground motion prediction equations (GMPEs), which are empirical models based on strong motion intensity parameters (e.g. PGA, PSA) computed from datasets of accelerograms and metadata from previous earthquakes on a region and then curve-fitted by regression analysis. The advantages of GMPEs, which are routinely applied in engineering applications, are that they are easy to use, rapid, and they can be easily understood by decision makers since they are based on observations. However, they present some major limitations:

• Lack of near-source records for large events (range where the potential damage to structures is larger), hence, predictions are poorly constrained in the range of magnitude and distance of particular concern for seismic design.

(20)

5

• Provide as output only peak values of ground motion parameters, rather than the full time-history, which are not useful for sophisticated engineering analysis (e.g. non-linear dynamic time history analyses).

• Implicit assumption that region based (from where GMPE are calibrated) and target region have similar characteristics and applies to generic or unknown situation, so cannot account for specific site conditions (e.g. complex site effects, such as alluvial basins). • they cannot provide an accurate description of the spatial correlation between peak

ground motion intensities at multiple sites and cross-correlation among different intensity measures, with potential impact for portfolio risk analyses.

On the other hand, with the increasing development of computational resources, physics-based numerical simulations (PBS) of earthquake ground motion are advocated as an alternative tool to cope with the previous limitations (Paolucci, et al., 2014) (Paolucci, et al., 2018) (POLIMI-Munich Re Contract, 2014), providing synthetic ground motion time-histories compatible with more or less realistic seismic source, propagation path and site response.

In this context, a joined research project has been established between Munich RE and Politecnico di Milano, with the objectives of developing a certified computer code to run numerical simulations of seismic wave propagation of large-scale models within high performance computer architecture and produce a set of physics-based ground motion scenarios in large urban areas exposed to high seismic risk. Among the set of urban areas to simulate, the city of Santiago de Chile was chosen.

Santiago is located in the central zone of Chile, at approximately latitude 33°27’S and longitude 70°40’W, around 100 km inland from the Pacific Ocean. The capital city of Chile has a population of 7.1 million in the metropolitan region, which represent the 40.5% of total Chilean population (INE, 2019), holding the executive power and the main concentration of infrastructure and economic activity of the country. Santiago de Chile is located to the south-west of the American continent and a significant part of its territory is in a subduction seismic environment between Nazca and South American Plates. The convergence rate of these plates is estimated in the range

(21)

6

of 65-90mm/year (Verdugo, et al., 2008), interaction that makes Chile one of the countries with the highest seismic rates in the world, with important events in the last decades, including the largest ground motion ever recorded (Mw 9.5 Valdivia Earthquake 1960) and the most recent in central Chile (Mw 8.8 Maule Earthquake). Despite the important seismic risk associated to the plate subduction zone, with a history of relevant events in the past in central Chile including Santiago area, such as Mw 8.2 Valparaiso Earthquake 1906 and Mw 8.0 Laguna Verde Earthquake 1985, this is not the only threat to the metropolitan area of Santiago, because of the presence of the San Ramón Fault (SRF), an active reverse fault system located along the eastern border of the Santiago Basin at the foot of the Andes mountain range. Studies of the morphological scarps along the San Ramón Fault indicates seismic ruptures in the recent past (Rauld-Plott, 2011), with two large earthquakes ruptures within the past 17,000-19,000 years, with the last event occurring approximately 8.000 year ago (Vargas, et al., 2014) possibly related to event of magnitude Mw 6.9 to Mw 7.4 (Rauld-Plott, 2011). The SRF represents therefore an active fault system, posing a relevant seismic threat to Santiago due to its proximity to the metropolitan area, and it has recently drawn attention by the local authorities.

1.2 Scope of this work

The main aim of this research is to generate and analyze different ground shaking scenarios originating from the San Ramón fault, using a 3D physics-based numerical simulation model. Starting from an existing numerical model by spectral elements (Paolucci, et al., 2013), several realistic fault rupture scenarios along the SRF, with magnitude ranging from 6 to 7, were generated and outputs were analyzed both in terms of spatial distribution of ground shaking parameters in the Santiago basin and synthetic time-history at specific, strategic locations in the city. Results of the 3D physics-based numerical simulations obtained with the open-source code SPEED are also compared with adequate empirical ground motion prediction equations from the literature. A discussion of the results of this work and the actual Chilean seismic regulation is included.

(22)

7

1.3 Organization of this work

This thesis report contains six chapters organized as follows.

Chapter 1 is the motivation of this work, describing the context and importance of this research. Chapter 2 gives a general framework of definitions in order to set the background necessary to understand where this work stands.

Chapter 3 explains the key concepts of ground motion prediction, the main aspects of 3D physics-based numerical simulation, the characteristics and potentialities of the software used for this project, SPEED, and mention some other case study covered by this project.

Chapter 4 will describe the case study of Santiago de Chile and the San Ramón Fault in detail, explaining the characteristics of the model and scenarios to be considered for this work.

Chapter 5 will summarize the results obtained from the 3D numerical simulations, ground motion parameters maps, time-histories, amplitude spectra and comparison with ground motion prediction equation, commenting the main outcomes observed. A discussion of the results comparing with the actual Chilean seismic regulation will be covered in this section.

Chapter 6 will provide a conclusion of the key aspects of this research, including observations and outcomes form the results, adding future challenges to this case study.

(23)

8

2 Preliminary definitions

To better understand the role of earthquake ground motion prediction, an overview of the main concepts of seismic risk is necessary. Below, the fundamental definitions at the basis of seismic risk are provided.

There is no common accepted definition of risk, mostly because is a complex relationship or variables that change depending on the case study. According to the United Nations Office for Disaster Risk Reduction (UNISDR), risk is defined as “the potential loss of life, injury, destroyed or damaged assets which could occur to a system, society or community in a specific period of time, determined probabilistically as a function of hazard, exposure, vulnerability”. Risk it is also defined as the convolution of hazard, vulnerability and exposure (Lai, et al., 2009).

Each component of risk should be also defined following the Sendai Framework for Disaster Risk Reduction 2015-2030 (UNISDR, 2015):

Hazard: A potentially damaging physical event, phenomenon or human activity that may cause

the loss of life or injury, property damage, social and economic disruption or environmental degradation. Hazards can include latent conditions that may represent future threats and can have different origins: natural (geological, hydrometeorological or biological) or induced by human processes (environmental degradation, technological hazards).

Exposure: the property, people, ecosystem or environment that are threatened by the hazard

event.

Vulnerability: is how the element exposed to risk is prone to be negatively affected to an adverse

(24)

9

Figure 3: convolution of hazard, vulnerability and exposure. Seismic risk. (Lai, et al., 2009) The key elements of risk assessment are the following (Simmons, et al., 2017):

i. Identify the hazards which might affect the system or environment being studied. It should be done at an initial stage.

ii. Assess the likelihood or probability that hazards might occur. Inputs to this process include history, modelling, experience, corporate memory, science, experimentation and testing. In practice, events with a very low probability (e.g. meteor impact) are ignored, focusing on ones more likely to happen that can be either prevented, managed or mitigated.

iii. Determine the exposure to the hazard, i.e. who or what is at risk.

iv. Estimate the vulnerability of that hazard to the entity exposed in order to calculate the physical or financial impact upon that entity when the event occurs. This may be obtained by a review of historical events, engineering approaches and/or expert opinion

v. Estimate the potential financial and social consequences of an event of different magnitudes.

These general concepts and steps can be easily generalized for any kind of hazard. For the case of earthquakes, points i. and ii. are related to Seismic Hazard Assessment (SHA), the quantitative evaluation of the expected ground motion (or any associated phenomenon, such as ground failure) at a specific site and within a specific time. This task requires several datasets. These can include earthquake catalogues (historical and instrumental), geodetic estimates of crustal

(25)

10

deformation of active geological faults, seismotectonic features and paleo-seismicity (Silva, et al., 2017). The quality, accuracy and quantity of these input datasets will suggest the choice of methodology for SHA, which can be evaluated either by deterministic or probabilistic approach.

Deterministic Seismic Hazard Analysis (DSHA): predefined scenarios are identified for a specific

seismic source and controlling earthquake (the event that can produce the higher level of shaking traduced in ground motion parameters). This method appears to be simple and provides a straightforward framework for evaluation of worst-case ground motion (Kramer, 2014). However, does not provide information about the likelihood of occurrence (when and where) or the expected level of shaking for time interval. It involves subjective decisions that can require expert opinion of different scientist and engineers related to this study field.

Probabilistic Seismic Hazard Analysis (PSHA): All potential earthquakes scenarios are explicitly

considered along with their likelihood of occurrence. Generally, it includes mathematical formulation to account uncertainties in earthquake size, location and time of occurrence and the outputs relates various levels of ground shaking that may be observed at a site to their corresponding exceedance probabilities in a given time. In recent decades, PSHA has reached an evident level of maturity since its inception by Cornell (1968) and McGuire (1976). The flexibility of the probabilistic framework has contributed to the credibility of the method and acceptance by engineers, planners and regulatory bodies (Silva, et al., 2017).

A four-step process has been defined for both approaches according to Reiter (1990), which are presented in Figure 4 and Figure 5.

(26)

11

Figure 4: four-step process for DSHA (Kramer, 2014).

Figure 5: four-step process for PSHA (Kramer, 2014)

For DSHA the steps are:

Identification and characterization of earthquake source, considering geometry and potential.

(27)

12

Selection of controlling earthquake described in terms of its size and distance from the site, as so as the ground motion parameters depending on the distance described in step 2.

The hazard is defined at each site in terms of ground motion produced by the controlling earthquake.

Similarly, for PSHA the steps are:

Identification and characterization of earthquake source, considering geometry and probability distribution of the potential rupture locations within the source.

Characterization of temporal distribution of the earthquake recurrence. An average rate at which the earthquake of some magnitude will be exceeded

Ground motion produced at the site by earthquakes of any possible size in any possible point from the source, with the use of predictive relationships.

Probability of ground motion exceedance during a determined time period.

A key component of both DSHA and PSHA is the ground motion model, typically provided by Ground Motion Prediction Equations (GMPE). In this work, Physics-based numerical simulation will be presented as an advanced tool for ground motion prediction, alternative to GMPE, especially in the near-source region for large earthquakes.

(28)

13

3 Ground Motion Prediction.

3.1 Introduction

As it is illustrated in the previous section, ground motion prediction is a key element in the chain of both DSHA and PSHA. Therefore, for proper seismic hazard and risk assessment studies, it is of capital interest to get an accurate estimation of ground motion with the knowledge and resources available for a specific site to their maximum extent.

In the literature a rather extensive variety of methods developed along the years exist, but just a subset of them have reached general acceptance and common use nowadays. A comprehensive article describing the key aspects, input parameters, outcomes, strengths and weaknesses of EGMP techniques with research and practical use for median to strong ground motion in a comparative way was developed by Douglas and Aochi (2008). There are basically two approaches to the implementation of EGMP models: the physical approach, where a mathematical model is analytically based on physical principles, and the experimental approach, where a mathematical model not necessarily based on physical insight is fitted to experimental data. Additionally, hybrid approaches which combines elements of both philosophies have been proposed (Douglas, et al., 2008).

Figure 6 presents several EGMP models ordered according to its approximate date of development in a timeline (x axis) and level of detail of the outcomes (y axis). Lines between them indicate causal relationships in their developments, while boxes indicate techniques which are most used for both research and engineering practice.

In the following, two of these models, which are enclosed in blue circles in Figure 6 will be briefly described and discussed: (1) Empirical ground motion models or Ground Motion Prediction Equations (GMPEs) because of its extensive use and acceptance and (2) the Spectral Element Method, which belongs to the family of physics-based numerical simulations (PBS); more specifically, the 3D PBS approach will be addressed (3DPBS) because it is the method adopted in this work.

(29)

14

Figure 6: GMP models timeline, level of detail and relationship (Douglas, et al., 2008).

3.2 Ground Motion Prediction Equations (GMPEs)

3.2.1

General description

Also called attenuation relationships, GMPEs provide means of predicting the level of ground shaking in a given site based on earthquake magnitude, source-to-site distance, local soil conditions and fault mechanism, among others. GMPEs are efficiently used to estimate ground motions parameters such as peak values and spectral ordinates for both deterministic and probabilistic seismic hazard analyses. First publications of these equations date back to the middle of decade of 60’s, with the pioneering work of Esteva and Rosenblueth (1964). Since then, the development of empirical relationships has enormously increased, with approximately 450 GMPEs available nowadays for estimating Peak Ground Acceleration - PGA (Douglas, 2018). Due to their empirical basis and good time gap since their creation, many GMPEs have been tested and validated with new events, becoming a widely accepted tool for seismic hazard assessment for both research, engineering and decision-making purposes.

Several efforts have been done to construct extensive and comprehensive datasets of GMPEs based on earthquake accelerometers databases, such as NGA-West, NGA-West2, NGA-East

(30)

15

projects (https://peer.berkeley.edu/) in USA or RESORCE in Europe ( http://www.resorce-portal.eu/). Other works, such as The Ground motion prediction equations 1964-2018 (Douglas, 2018)(http://www.gmpe.org.uk/) provides a compendium with about 450 GMPEs for PGA and 290 GMPEs for response spectral ordinates.

Among them, the one adopted for this study will be described in the following.

3.2.2

GMPE after Cauzzi et al. 2015 (CAEA15)

This is an empirical prediction of 5%-damped elastic response spectra in the period range 0-10s for Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV), based on a global dataset of more than 1,880x2 orthogonal horizontal digital accelerometers records with site-to-source distance or distance from rupture RRUP < 150km from 98 global earthquakes with 4.5 ≤ Mw ≤ 7.9

(Cauzzi, et al., 2015).

The predictive model is presented as follows

𝑙𝑜𝑔₁₀𝑦 = 𝑓_𝑀+ 𝑓_𝑅+ 𝑓_𝑆 + 𝑓_𝑆𝑂𝐹 + 𝜀 Where 𝑓_𝑀 = 𝑐₁+ 𝑚₁𝑀_𝑊+ 𝑚₂𝑀_𝑊2 𝑓_𝑅 = (𝑟₁+ 𝑟₂𝑀_𝑊)𝑙𝑜𝑔₁₀(𝑅_𝑅𝑈𝑃+ 𝑟₃) 𝑓𝑆 = 𝑠𝐵𝑆𝐵+ 𝑠𝐶𝑆𝑐 + 𝑠𝐷𝑆𝐷, 𝑜𝑟 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒𝑙𝑦 𝑓𝑆 = 𝑏𝑉𝑙𝑜𝑔10( 𝑉_𝑆,30 𝑉𝐴 ) , 𝑜𝑟 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒𝑙𝑦 𝑓_𝑆 = 𝑏_𝑉800𝑙𝑜𝑔₁₀(𝑉𝑆,30 800) 𝑓_𝑆𝑂𝐹 = 𝑓_𝑁𝐹_𝑁+ 𝑓_𝑅𝐹_𝑅+ 𝑓_𝑆𝑆𝐹_𝑆𝑆

y can be either the horizontal 5%-damped displacement response spectrum DRS (T; 5%) in cm, PGA (cm s-2_{) or PGV (cm s}-1_{). Prediction of pseudo-spectral values can be obtained as PSA (T; 5%)}

(31)

16

= DRS (T; 5%)x(4π/T2_{) and PGA}_~_{PSA (0.01s; 5%). The horizontal component of ground motion}

is represented by the geometric mean of the orthogonal horizontal values. Parameters of equations above are: c1 = -2.19617, m1 = 0.52375, m2 = -0.06094, r1 = -3.80190, r2 = 0.35508, sB =

0.2107, sC = 0.28251, sD = 0.28288, bV = -0.31007, bV800 = -0.70244, VA = 2319.18598, fN = -0.02411,

fR = 0.07246, fSS = -0.05632. ε is a random term assumed normally distributed with zero mean and

standard deviation σ(𝑙𝑜𝑔10𝑦), given by the combination 𝜎 = √𝜑2+ 𝜏2, where φ is an intra-event

component equal to 0.25892 and τ is an inter-event component equal to 0.22145.

• Three alternatives for site term fS are presented. Mean values of 𝑉𝑆,30 is 365 m/s. Either

use directly 𝑉_𝑆,30 values to characterize sites or four Eurocode 8 site classes described below (EUROCODE 8, 2012):

A Rocklike, 𝑉𝑆,30 ≥ 800 m/s. 7% of data. SB = SC = SD = 0.

B Stiff, 360 ≤ 𝑉𝑆,30 < 800 m/s. 43% of data. SB = 1, SC = SD = 0.

C Soft, 180 ≤ 𝑉𝑆,30 < 360 m/s. 40% of data. SC = 1, SB = SD = 0.

D Very Soft, 𝑉𝑆,30 < 180 m/s. 10% of data. SD = 1, SB = SC = 0.

• Use three faulting mechanisms using classification of Boore and Atkinson (2008): Normal 20 earthquakes. FN = 1, FR = FSS = 0.

Strike-slip 43 earthquakes. FSS = 1, FN = FR = 0.

Reverse 26 earthquakes. FR = 1, FN = FSS = 0.

(32)

17

3.3 3D Physics-Based Numerical Simulation

3.3.1

General description

This approach to predict ground motion equations belongs to the family of numerical methods to solve the equations of wave propagation in solid materials. In general, this family includes different numerical methods, such as Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), Lattice Particle Method (LPM) and Spectral Element Method (SEM). Each of them has its advantages and drawbacks mostly related to computational performance and accuracy of results. In Douglas and Aochi (2008) the most relevant numerical methods are presented in a comparative way. All these numerical methods have considerably evolved in the last decade driven by the increasing power of parallel computing on multi-core clusters, becoming an attractive option to produce reliable physics-based earthquake ground motion scenarios, in the presence of realistic 3D configurations of seismic source, complex basins and topographic features. Their development was significantly boosted in the last 10 years by international benchmark (or verification) exercises, such as the ShakeOut (Bielak, et al., 2010) and Grenoble (Chaljub, et al., 2010) benchmarks. The first project performed three simulations of a Mw 7.8 earthquake scenario on a portion of San Andreas fault in southern California using finite difference methods and finite element methods, while the last mentioned developed numerical simulations of ground motion in a typical alpine valley with complex 3D geometry and large velocity contrast.

Relatively few numerical codes exist for this purpose, mostly belonging to finite difference and finite element methods, while high order accurate finite element methods (i.e. spectral element method) have emerged later as an alternative powerful technique, relying on a balance between accuracy, ease of implementation and parallel efficiency (POLIMI-Munich Re Contract, 2014). Four open source codes belong to the family of spectral elements and finite volume method are available, which are:

SPECFEM3D (https://geodynamics.org/cig/software/specfem3d/). EFISPEC (http://efispec.free.fr).

(33)

18

SeisSol (https://www.geophysik.uni-muenchen.de/~kaeser/SeisSol/). SPEED (http://speed.mox.polimi.it/).

This study has adopted the last computer code, of which an overview of main characteristics is introduced in the following section.

3.3.2

SPEED: Spectral Elements in Elastodynamics with Discontinuous Garlekin

SPEED is an open-source code suitable to address the general problem of Elastodynamics in arbitrarily complex media (Mazzieri, et al., 2013). This code is designed for simulation of large seismic wave propagation problems including coupled effect of seismic fault rupture, propagation path through Earth’s layer, localized geological irregularities such as alluvial basins and topographic irregularities. Also, it is possible to represent soil structure interaction and presence of extended structures, such as railway viaducts, tunnels or high buildings, as is illustrated in Figure 7.

Figure 7: simulation scheme of SPEED (Paolucci, et al., 2018).

A non-conforming mesh strategy implemented through a Discontinuous Garlekin (DG) approach (h-adaptivity) and non-uniform polynomial approximation degrees (N-adaptivity) allows to treat numerical problems with large range of spatial dimensions, making the mesh more flexible,

(34)

19

permitting to select best-fitted discretization parameters in each subregion, while controlling overall accuracy of approximation. Physical discontinuities can be modeled either by DG approach (with physical interphases) or by non-honoring technique (where material properties are given node by node). Time integration can be performed either by explicit second-order Leap-Frog scheme or explicit fourth-order Runge-Kutta method. SPEED is designed for multi-core computers or large clusters. It takes advantage of hybrid parallel programing based on Message Passing Interface (MPI) and OpenMP library for multi-threading operations of shared memory. The mesh may be constructed using third party software, e.g. CUBIT (https://cubit.sandia.gov/) (Mazzieri, et al., 2013).

Among the main features of SPEED is that allow users to treat with different seismic excitation modes, including extended seismic fault rupture and plane wave load, different boundary conditions, such Dirichlet and/or Neumann boundary conditions, along with absorbing paraxial boundary conditions to prevent propagation of spurious reflections from external boundaries of the computational domain. Also, SPEED considers:

• Treatment of kinematic finite-fault models, featuring several options to model an arbitrary complex seismic source, assigning realistic distributions of co-seismic slip (e.g. (Crempien, et al., 2015), (Herrero, et al., 1994)) along an extended fault plane through proper pre-processing tools (see Figure 8).

Figure 8: kinematic modelling of seismic source (Paolucci, et al., 2018).

• Dynamic rupture modeling of seismic source, where the fault is defined as an internal planar interface across which discontinuities with the soil domain are allowed, and static/dynamic friction conditions are implemented.

• Attenuation Model of visco-elastic media using constant damping, frequency dependent quality factor (Q=Q0f) and Rayleigh damping.

(35)

20

• Non-linear elastic soil behavior (NLE) soil model through generalization to 3D load conditions of 1D linear equivalent approach of modulus soil reduction (G-γ) and damping (D- γ) curves (Kramer, 2014), where G, D and γ are the shear modulus, damping ratio and 1D shear strain, respectively.

Due to computational limitations for such large SE models as well as insufficient resolution of geologic and seismic source models, the accuracy of 3DPBNS is typically restricted to the low frequency range, up to about 1.5-2.0 Hz. Therefore , to enrich the frequency range and make it suitable for engineering applications (0-25 Hz), broadband ground motions have to be generated starting from the low-frequency waveforms produced by the numerical simulations. For this reason, a post processing stage of the SPEED results is implemented a broadband ground motion using Artificial Neural Networks (ANN) (Paolucci, et al., 2018), which consist in: (1) training an ANN based on a set of strong motion records dataset (namely SIMBAD) consisting in about 500 records with Mw 5-7.3 and epicentral distances up to 35km, to predict short period spectral ordinates (T<T*) based on long period ones(T>T*), (2) for each simulated waveform, an ANN to broadband (ANN2BB) response spectrum is computed, using long period ordinates from simulations, while short period ordinates from the ANN. (3) The simulated low-frequency waveform is enriched in the high-frequency by a stochastic contribution, characterized by the magnitude and source-to-site distance of the scenario earthquake. (4) The hybrid PBS-stochastic waveform is iteratively modified in the frequency domain with no phase change, until its response spectrum matches the target ANN2BB spectrum (Figure 9).

This code has been verified through benchmark solutions, such as 3D seismic response of Los Angeles basin, Grenoble, Euroseistest site, Cybershake and ShakeOut projects (Mazzieri, et al., 2013) and it has been validated for simulations of real earthquakes, such as L’aquila, Po Plain, Marsica and Thessaloniki earthquakes, between others (http://speed.mox.polimi.it/ ). To get more details about the software and the study cases done within SPEED project, the reader is referred to (POLIMI-Munich Re Contract, 2014), (Infantino, 2016), (Infantino, et al., 2018), (Paolucci, et al., 2018), (Paolucci, et al., 2016), (Smerzini, et al., 2018), (Smerzini, et al., 2017).

(36)

21

Figure 9: scheme of construction of broadband response using ANN (Paolucci, et al., 2018).

The general workflow of ground shaking maps using SPEED can be seen in Figure 10.

(37)

22

4 The case of San Ramón Fault in Santiago de Chile

4.1 Seismological Background of North and Central Chile.

As it was introduced in chapter 1, Santiago de Chile is potentially affected by more than one seismic source. The main extension of the country, around 3,200km (of a total length of 4,200km) from northern limit with Peru to Penas gulf in south Chile, is at the margin of the junction of the oceanic Nazca and continental South American plates, as it can be seen in Figure 11, where the first one moves towards and submerge beneath the second one at a range of 60-90mm/year. This phenomenon produce the namely subduction zone, where the movement and submergence of Nazca plate induces a seismically and volcanic active environment. A typical section of a subduction zone is presented in Figure 12, in the slope area is where the friction forces increases in time due to the relative movement of the plates, cumulating elastic energy and releasing it through a co-seismic movement when a threshold stress is reached. In Figure 13 the types of earthquakes threatening the north, central and mid-south zone of Chile, including the city of Santiago, are schematically illustrated in Figure 13 and described below.

Figure 11: tectonic plates in Chile. The not-labeled blue plate on bottom correspond to the Antarctic plate, which defines the seismic hazard in the southern zone of Chile.

(38)

23

Figure 12: typical continental subduction zone section.

Figure 13: types of earthquakes in central zone of Chile. National Seismologic Center http://www.csn.uchile.cl . a. Inter-plate earthquakes (< 40-60 km depth): produced at the frictional contact between

the two plates, when net compressive horizontal strength in the contact zone (or coupled zone) between Nazca and South America plate is higher than the mechanical couple friction between them. This type is also known as “subduction earthquakes”. They behave with inverse fault mechanism and its magnitude is proportional to the slip and slipping area. When this type of earthquake triggers at high magnitude, usually presents vertical displacement of the ocean floor, with high probabilities of producing tsunamis. Examples of this type of earthquakes is the Mw 9.5 Valdivia Earthquake 1960 and Mw 8.8 Maule Earthquake 2010.

b. Intra-plate earthquake of intermediate depth (> 50 km, < 250 km depth): occurs at interior of the Nazca plate, because of the high stresses and brittle behavior of the plate. It has been observed that these earthquakes are more damaging that inter-plate earthquakes

(39)

24

of similar magnitude. Examples of this events are the Mw 8.0 Chillán Earthquake 1939 (the event with highest number of victims in Chilean history) and Mw 7.1 Punitaqui Earthquake 1997.

c. Shallow or crustal Earthquakes (< 60 km depth): occurs in the crust inside the South American plate, due to deformations provoked by the convergence between Nazca and South American plate. These deformations gave origin to the Andes Mountain Range and generally are maximum close to them. Examples of these earthquakes are the Mw 6.6 Curicó Earthquake 2004, Ms 6.9 Las Melosas Earthquake 1958 and Mw 6.3 Chusmiza Earthquake 2001. In this category are the scenarios of the San Ramón Fault.

d. Outer-rise earthquakes (< 30 km depth): occurs off shore of the Chilean Trench. Their origin is due to the deformation of Nazca plate and bending stresses on it before its subduction, locating in the outer-rise or maximum curvature zone. These earthquakes a generally shallow and in general its magnitude are less than Mw 7.0, main reason why this events generally don’t produce tsunamis. An example of this type of earthquakes are the Mw 6.7 off-shore Valparaiso Earthquake 2001.

Type (a) and (b) earthquake have been widely studied by academic sector and have been properly introduced in seismic design regulation due to its higher frequency and proved consequences, and (d) type generally does not represent significant threats to the population. In spite of recent cases of the type (c) earthquakes in Chile, they occurred in scarcely populated areas, not giving a meaningful sense of urgency to consider this type of earthquakes for seismic hazard assessment in Chile. Armijo et al. (2010) descrived this situation as follows: “Seismic hazard assessment in Chile has been widely studied for subduction earthquakes, because they are predominant in the seismic environment of the country, therefore the cortical structures appears to be currently minimized”. From a seismic risk point of view, however, as it was introduced in Chapter 2, not only the seismic hazard affect the seismic risk in an area, but the latter depends also on the vulnerability and exposure factors, which are clearly increased when speaking about a large metropolis like Santiago.

4.2 The San Ramón Fault (SRF) in Santiago de Chile.

The first study of this geological fault was done by Rauld in 2002 as a graduation project to get professional degree of Geologist, demonstrating the characteristic of active inverse fault, its dimensions, locations and first estimating a Mw 6.3 as maximum potential earthquake. Lately, the same author (Rauld-Plott, 2011) performed a comprehensive study of the fault as a Ph.D. Thesis in Geological Science, where a novel understanding of the West Andean Thrust (WAT) was proposed as a first order tectonic element in the Andes and the SRF was interpreted as an evolving element in this context, capable of producing earthquakes up to a maximum credible magnitude of Mw 7.4. The chapter 5 of his work corresponds to the article where the SRF is

(40)

25

illustrated from a geological point of view (Armijo, et al., 2010) and served as a key input to characterize the seismic source of this research.

Later geological and paleo-seismic studies have attributed two historical events to the SRF in the range of 17-19 k.y. and ~8k.y., with displacements of 5 m in each event and an estimated Mw 7.5, estimating PGA in the footwall of 0.5 g using GMPE after Abrahamson et al (2008) (Vargas, et al., 2014) (Vargas G., 2012). A historiographic evolution of the exposure of Santiago to the SRF and its relationship to the Santiago 1647 earthquake was performed in (Aránguiz, 2018) from an urban planning point of view, giving a warning about its real threat to the city.

The SRF is an inverse fault system expressed by a semi-continuous scarp extended 35-40 km from north to south from Río Mapocho to south of Río Maipo and 12 km depth until the Eastward Tilted Marginal Block (Armijo, et al., 2010), with an average dip angle value of 60°. In Figure 14 it is possible to see a general 3D view of the WAT and part of the Santiago basin, a black rectangle is present with a general location of the map of the SRF in top view shown in Figure 15 and the red line indicates a geological elevation presented in Figure 16.

(41)

26

(42)

27

Figure 16: geological elevation of the WAT and SRF (Armijo, et al., 2010).

4.3 Santiago Basin model for SPEED (CHL-SAN)

The simulation of the Santiago area for hypothetical earthquakes occurring along the SRF was performed in the context of POLIMI – Munich Re joined research activity. The city was selected because of its high seismic risk, proper characterization of its seismic source (SRF) and available 3D geological and geophysical data describing the deep and sub-surface velocity structure, (Pilz, et al., 2010) and (PIlz, et al., 2011).

In the work of Pilz et al. (2010) a 3D shear wave velocity model for Santiago basin was proposed based on 146 ambient noise recordings in 125 sites of the northeastern part of the basin, from where was obtained the horizontal-to-vertical spectral ratios (H/V) of each single station with the Nakamura technique (Nakamura, 1989) and then inverted to obtain the S-wave velocity profile at each specific site, using as constraints for the sedimentary layer thickness values obtained from gravimetric measurements after Araneda et al. (2000) (See Figure 19). Each local S-wave velocity profile was then resampled with a spatial resolution of 1m and 100m of horizontal spatial resolution to obtain a 3D S-wave velocity model. The model contains detailed description of the sedimentary basin shape defined by the S-wave velocity changes between sediment and bedrock, as well as the orography based on digital elevation data. For the interpolation of the spatially changing S-wave velocities, Kriging technique was employed, and its performance tested using cross validation after Isaaks and Srivastaba (1989). Due to sediment thickness and S-wave velocities has the major influences in H/V spectrum, P-wave velocity of Vp=1.11Vs+1290 [m/s]

(43)

28

was used (Kitsunezaki et al., 1990). Figure 18 on top shows the studied area from where was derived the 3D shear wave model and 4 sections which are shown below with the bedrock level in grey and different values of VS in color bar.

Later, Pilz et al (2011) developed a 3D model of the Santiago basin including 1D variable in depth S-wave velocity fitting with the model performed from microtremors, P-wave velocity profile variable in depth consistently with Kitsunezake et al. (2011) and depth dependent of density from Bravo (1992). The crustal model was assumed as a 3 cake-layered structure with constant values according to Godoy (1999) and Barrientos et al. (2004). The smooth vertical variation inside the basin was considered, assigning to each Legendre-Gauss-Lobato node the mechanical properties prescribed. A summary of this expressions and values can be seen in Figure 17.

Figure 17: Santiago model with size, wave velocities, density and quality factors specifications (POLIMI-Munich Re Contract, 2014).

(44)

29

Figure 18: on top, basin of Santiago de Chile, in the back rectangle the study area of Pilz et al (2010) and the the black lines are section of the 3D shear wave model with bedrock level in grey and Vs values in colors shown below.

(45)

30

Figure 19: Thickness of sedimentary cove of the basin of Santiago de Chile shown in color bar, determined by interpolation of gravimetric data (PIlz, et al., 2011).

The mesh domain of 77.6 x 97.4 x 19 km is composed by a hexahedral conforming SE mesh, designed to propagate up to maximum frequencies of about 1.5 Hz, with 1,108,895 elements and a total number of 31,050,124 nodes for polynomials of degree 3. A more refined discretization sizes were used (hexahedral sides with a minimum of 60m) in order to get better representation in the sub surface and surface layers characterized by relatively low shear-wave velocities (see Figure 20 left). Because of the minimum element size and the polynomial degree, a minimum of 4 points per wavelength are necessary for accurate numerical results. A set of 13,814 points on

(46)

31

the surface nodes of the model were located on an almost-regular array with a minimum distance of around 600m and maximum of 1300m between them, in order to measure the synthetic time-histories obtained from SPEED, hereafter will be called monitors (see Figure 20 right).

Figure 20: model elevation view with mesh relative sizes (left). Model plant view with monitors distributions (right). In agreement to (Armijo, et al., 2010) a simplified model of the SRF was assumed. The source parameters are the following: reverse fault with rake or slip angle of 90, dip angle of 60°, and strike angle of 353°. The maximum rupture area considered is of 40km length and 20 width, creating a maximum scenario of around Mw 7.1 (see Figure 21).

(47)

32

Figure 21: 3D view of SRF in Santiago model.

As it was explained in section 3.3.2, SPEED considers two soil response models: a linear visco-elastic model (LE) and a non-linear visco-elastic model (NLE). As a matter of fact, it has been observed that a soil subjected to strong ground shaking exhibits a non-linear behavior, with decrease of its shear modulus and increases in damping ratio with increasing shear strain. This can be described by a linear-equivalent model, as explained in (Kramer, 2014) (see Figure 22).

Figure 22: linear equivalent model for shear modulus reduction (Kramer, 2014).

Santiago soil is characterized by a rather stiff soil in surface in most of its basin surface, as it can be seen in Figure 23 (Leyton, et al., 2010). Here is described a dominant presence of soil type I

(48)

33

(Rock) type II (gravel and sandy gravel) and IIIa (sub angular gravel blocks in supporting sandy-clayey matrix) and IIIb (gravel and gravel blocks in sandy-sandy-clayey matrix). Notice that the geological characterization agrees with the wave velocity model defined previously. The black contour determines the urban areas limits, which nicely represents the basin contour of the Santiago SPEED model, especially in east part of the basin, which is the closest region to the seismic source.

Figure 23: surface geology of Santiago basin (Leyton, et al., 2010).

Considering this soil characteristics distribution, a general coarse gravel (GW) behavior of the basin soil is assumed for the NLE simulations, with shear modulus reduction and damping ratio curves according to the work of (Rodriguez, et al., 1995) on cyclic dynamic loading test of granular soil of Santiago de Chile (see Figure 24). For the Santiago basin model, an average value from this

(49)

34

research was used, employing 13 point later included as input for SPEED, which are interpolated within the routine. Some simulations were generated assuming linear visco-elastic behavior, while others with greater magnitude were done with this non-linear visco-elastic approach, as it will be described in the following section.

Figure 24: shear modulus reduction and damping ratio increase for granular soils (Rodriguez, et al., 1995). Red lines indicates non-linear visco-elastic behavior adopted for this study.

4.4 Seismic Scenarios

A set of seismic scenarios have been realized for this study, considering as variable parameters, the earthquake magnitude (Mw), if is purely linear visco-elastic (LE) or non-linear visco-elastic within the basin (NLE), the seismic rupture model, according to Crempien-Archuleta (ARC) (Crempien, et al., 2015) or Herrero-Bernard (HER) (Herrero, et al., 1994),

(50)

35

The seismic scenarios are summarized in Table 2.

Table 2: seismic scenarios description. HER refers to Herrero and Bernard (1994) rupture generator.

Scenario Name ID name Moment magnitude [Mw] basin behavior Rupture Model Cutoff freq. fc [Hz] Notes

E00011 E11 7.0 LE HER 1.5 shallow hypocenter and slip distribution

E00013 E13 7.0 LE HER 1.5

deeper hypocenter and slip distribution to avoid super shear effect

E00014 E14 7.0 NLE HER 1.5

deeper hypocenter and slip distribution to avoid super shear effect

E00015 E15 6.0 LE HER 1.5 Deep hypocenter, to contrast with E00001

E00016 E16 6.5 LE HER 1.5 Deep hypocenter, to contrast with E00002

E00020 E20 6.0 LE HER 1.5 scenarios performed in a previous study

3D physics-based numerical scenarios for earthquake strong ground motion prediction : the case of the San Ramon fault in Santiago de Chile basin

iii

v

Acknowledgement

vi

vii

Abstract

viii

ix

Contents

x

xi

List of Figures

xii

xiii

xiv

xv

List of Tables

1

1 Introduction

1.1

Motivation

2

3

4

5

6

1.2

Scope of this work

7

1.3

Organization of this work

8

2 Preliminary definitions

9

10

11

12

13

3 Ground Motion Prediction.

3.1

Introduction

14

3.2

Ground Motion Prediction Equations (GMPEs)

General description

15

GMPE after Cauzzi et al. 2015 (CAEA15)

16

17

3.3

3D Physics-Based Numerical Simulation

General description

18

SPEED: Spectral Elements in Elastodynamics with Discontinuous Garlekin

19

20

21

22

4 The case of San Ramón Fault in Santiago de Chile

4.1

Seismological Background of North and Central Chile.

23

24

4.2

The San Ramón Fault (SRF) in Santiago de Chile.

25

26

27

4.3

Santiago Basin model for SPEED (CHL-SAN)

28

29

30

31

32

33

34

4.4

Seismic Scenarios